Total external reflection is a phenomenon traditionally involving X-rays and extreme ultraviolet, but in principle any type of electromagnetic or other wave, closely related to total internal reflection.

Total internal reflection describes the fact that radiation (e.g. visible light) can, at certain angles, be totally reflected from an interface between two media of different indices of refraction (see Snell's law). Total internal reflection occurs when the first medium is optically denser than the second medium, and the incident angle is larger than the critical angle of the medium, for example, light that starts in water and bounces off the water-to-air interface.

, being comparable to, or larger than most atomic binding frequencies in a material. The refractive index can be written as the square root of the dielectric function for relative permittivity from the Lorentz oscillator model (in SI units):

is the imaginary unit scattering electrons. The critical angle, the refracted ray travels exactly parallel to the surface, as a limit of Snell's law. In terms of a grazing incidence angle, defined relative to a surface, this can be written as

, Fresnel reflectivity as an extinction coefficient shows that the refracted ray penetrates slightly into the material, leading to reflective losses from absorption. makes it possible to focus X-rays, as in a Wolter telescope.

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